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import numpy as np
from numpy.linalg import inv, lstsq
from numpy.linalg import matrix_rank as rank
from numpy.linalg import norm
class MatlabCp2tormException(Exception):
def __str__(self):
return 'In File {}:{}'.format(__file__, super.__str__(self))
def tformfwd(trans, uv):
"""
Function:
----------
apply affine transform 'trans' to uv
Parameters:
----------
@trans: 3x3 np.array
transform matrix
@uv: Kx2 np.array
each row is a pair of coordinates (x, y)
Returns:
----------
@xy: Kx2 np.array
each row is a pair of transformed coordinates (x, y)
"""
uv = np.hstack((uv, np.ones((uv.shape[0], 1))))
xy = np.dot(uv, trans)
xy = xy[:, 0:-1]
return xy
def tforminv(trans, uv):
"""
Function:
----------
apply the inverse of affine transform 'trans' to uv
Parameters:
----------
@trans: 3x3 np.array
transform matrix
@uv: Kx2 np.array
each row is a pair of coordinates (x, y)
Returns:
----------
@xy: Kx2 np.array
each row is a pair of inverse-transformed coordinates (x, y)
"""
Tinv = inv(trans)
xy = tformfwd(Tinv, uv)
return xy
def findNonreflectiveSimilarity(uv, xy, options=None):
options = {'K': 2}
K = options['K']
M = xy.shape[0]
x = xy[:, 0].reshape((-1, 1)) # use reshape to keep a column vector
y = xy[:, 1].reshape((-1, 1)) # use reshape to keep a column vector
tmp1 = np.hstack((x, y, np.ones((M, 1)), np.zeros((M, 1))))
tmp2 = np.hstack((y, -x, np.zeros((M, 1)), np.ones((M, 1))))
X = np.vstack((tmp1, tmp2))
u = uv[:, 0].reshape((-1, 1)) # use reshape to keep a column vector
v = uv[:, 1].reshape((-1, 1)) # use reshape to keep a column vector
U = np.vstack((u, v))
# We know that X * r = U
if rank(X) >= 2 * K:
r, _, _, _ = lstsq(X, U, rcond=-1)
r = np.squeeze(r)
else:
raise Exception('cp2tform:twoUniquePointsReq')
sc = r[0]
ss = r[1]
tx = r[2]
ty = r[3]
Tinv = np.array([[sc, -ss, 0], [ss, sc, 0], [tx, ty, 1]])
T = inv(Tinv)
T[:, 2] = np.array([0, 0, 1])
return T, Tinv
def findSimilarity(uv, xy, options=None):
options = {'K': 2}
# uv = np.array(uv)
# xy = np.array(xy)
# Solve for trans1
trans1, trans1_inv = findNonreflectiveSimilarity(uv, xy, options)
# Solve for trans2
# manually reflect the xy data across the Y-axis
xyR = xy
xyR[:, 0] = -1 * xyR[:, 0]
trans2r, trans2r_inv = findNonreflectiveSimilarity(uv, xyR, options)
# manually reflect the tform to undo the reflection done on xyR
TreflectY = np.array([[-1, 0, 0], [0, 1, 0], [0, 0, 1]])
trans2 = np.dot(trans2r, TreflectY)
# Figure out if trans1 or trans2 is better
xy1 = tformfwd(trans1, uv)
norm1 = norm(xy1 - xy)
xy2 = tformfwd(trans2, uv)
norm2 = norm(xy2 - xy)
if norm1 <= norm2:
return trans1, trans1_inv
else:
trans2_inv = inv(trans2)
return trans2, trans2_inv
def get_similarity_transform(src_pts, dst_pts, reflective=True):
"""
Function:
----------
Find Similarity Transform Matrix 'trans':
u = src_pts[:, 0]
v = src_pts[:, 1]
x = dst_pts[:, 0]
y = dst_pts[:, 1]
[x, y, 1] = [u, v, 1] * trans
Parameters:
----------
@src_pts: Kx2 np.array
source points, each row is a pair of coordinates (x, y)
@dst_pts: Kx2 np.array
destination points, each row is a pair of transformed
coordinates (x, y)
@reflective: True or False
if True:
use reflective similarity transform
else:
use non-reflective similarity transform
Returns:
----------
@trans: 3x3 np.array
transform matrix from uv to xy
trans_inv: 3x3 np.array
inverse of trans, transform matrix from xy to uv
"""
if reflective:
trans, trans_inv = findSimilarity(src_pts, dst_pts)
else:
trans, trans_inv = findNonreflectiveSimilarity(src_pts, dst_pts)
return trans, trans_inv
def cvt_tform_mat_for_cv2(trans):
"""
Function:
----------
Convert Transform Matrix 'trans' into 'cv2_trans' which could be
directly used by cv2.warpAffine():
u = src_pts[:, 0]
v = src_pts[:, 1]
x = dst_pts[:, 0]
y = dst_pts[:, 1]
[x, y].T = cv_trans * [u, v, 1].T
Parameters:
----------
@trans: 3x3 np.array
transform matrix from uv to xy
Returns:
----------
@cv2_trans: 2x3 np.array
transform matrix from src_pts to dst_pts, could be directly used
for cv2.warpAffine()
"""
cv2_trans = trans[:, 0:2].T
return cv2_trans
def get_similarity_transform_for_cv2(src_pts, dst_pts, reflective=True):
"""
Function:
----------
Find Similarity Transform Matrix 'cv2_trans' which could be
directly used by cv2.warpAffine():
u = src_pts[:, 0]
v = src_pts[:, 1]
x = dst_pts[:, 0]
y = dst_pts[:, 1]
[x, y].T = cv_trans * [u, v, 1].T
Parameters:
----------
@src_pts: Kx2 np.array
source points, each row is a pair of coordinates (x, y)
@dst_pts: Kx2 np.array
destination points, each row is a pair of transformed
coordinates (x, y)
reflective: True or False
if True:
use reflective similarity transform
else:
use non-reflective similarity transform
Returns:
----------
@cv2_trans: 2x3 np.array
transform matrix from src_pts to dst_pts, could be directly used
for cv2.warpAffine()
"""
trans, trans_inv = get_similarity_transform(src_pts, dst_pts, reflective)
cv2_trans = cvt_tform_mat_for_cv2(trans)
return cv2_trans
if __name__ == '__main__':
"""
u = [0, 6, -2]
v = [0, 3, 5]
x = [-1, 0, 4]
y = [-1, -10, 4]
# In Matlab, run:
#
# uv = [u'; v'];
# xy = [x'; y'];
# tform_sim=cp2tform(uv,xy,'similarity');
#
# trans = tform_sim.tdata.T
# ans =
# -0.0764 -1.6190 0
# 1.6190 -0.0764 0
# -3.2156 0.0290 1.0000
# trans_inv = tform_sim.tdata.Tinv
# ans =
#
# -0.0291 0.6163 0
# -0.6163 -0.0291 0
# -0.0756 1.9826 1.0000
# xy_m=tformfwd(tform_sim, u,v)
#
# xy_m =
#
# -3.2156 0.0290
# 1.1833 -9.9143
# 5.0323 2.8853
# uv_m=tforminv(tform_sim, x,y)
#
# uv_m =
#
# 0.5698 1.3953
# 6.0872 2.2733
# -2.6570 4.3314
"""
u = [0, 6, -2]
v = [0, 3, 5]
x = [-1, 0, 4]
y = [-1, -10, 4]
uv = np.array((u, v)).T
xy = np.array((x, y)).T
print('\n--->uv:')
print(uv)
print('\n--->xy:')
print(xy)
trans, trans_inv = get_similarity_transform(uv, xy)
print('\n--->trans matrix:')
print(trans)
print('\n--->trans_inv matrix:')
print(trans_inv)
print('\n---> apply transform to uv')
print('\nxy_m = uv_augmented * trans')
uv_aug = np.hstack((uv, np.ones((uv.shape[0], 1))))
xy_m = np.dot(uv_aug, trans)
print(xy_m)
print('\nxy_m = tformfwd(trans, uv)')
xy_m = tformfwd(trans, uv)
print(xy_m)
print('\n---> apply inverse transform to xy')
print('\nuv_m = xy_augmented * trans_inv')
xy_aug = np.hstack((xy, np.ones((xy.shape[0], 1))))
uv_m = np.dot(xy_aug, trans_inv)
print(uv_m)
print('\nuv_m = tformfwd(trans_inv, xy)')
uv_m = tformfwd(trans_inv, xy)
print(uv_m)
uv_m = tforminv(trans, xy)
print('\nuv_m = tforminv(trans, xy)')
print(uv_m)
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